the length of event $x$ has approximately an exponential distribution with a mean of 90 minutes. if event $x$ occurs $90$ times, how many times will the event last longer than $3$ hours?
My work so far:
here for exponential distribution parameter $β = 90$
$P$ (event occur after 3 hours (180 minutes)):
$$P(X>180)=1-P(X<180)=1-(1-\exp(-180/90))= 0.1353$$
therefore the number of events that last longer than $3$ hours
$$=np=90*0.1353= 12.177 \sim 12$$